A free plugin is available that reproduces some of this functionality.

Purpose

To have attachments open up in a new window or tab when clicking on them.

Solution

You need to add a TARGET = "_blank" to the <a href> HTML tag.

The A element used in HTML denotes an anchor which is a hypertext link. 
The HREF attribute specifies a hypertext link to another resource, such as an HTML document or a JPEG image.
The TARGET attribute is used with frames to specify the frame in which the link should be rendered. If no frame with such a name exists, the link is rendered in a new window unless overridden by the user. Special frame names begin with 
an underscore. The frame used in this document is the _blank which renders the link in a new, unnamed window.

Source: http://www.w3.org/TR/html401/struct/links.html

For example, by using the HTML code below, clicking on the link "a new window" will open the "newwindow.html" page in a new window:

<A href="newwindow.html" _TARGET="_blank"_>a new window</A>

Open attachments listed for a Space

To open the attachments listed from the Browse Space->Attachments tab, in a new window, the file <CONFLUENCE-INSTALL>/confluence/pages/listattachmentsforspace.vm has to be modified. Below are the listed steps:

1. Locate the following block of code in the listattachmentsforspace.vm file:

   #foreach ($attachment in $results)
            #set ($labels = $attachment.labels)
            #set ($labelable = $attachment)
            <tr id="attachment_$!attachment.id">
                  <td><a name="$!generalUtil.urlEncode($!attachment.content.displayTitle)-attachment-$!generalUtil.urlEncode($!attachment.fileName)">#parse ("/pages/includes/attachment_icon.vm")</a> <a href="$req.contextPath$!attachment.downloadPathWithoutVersion">$generalUtil.shortenString($attachment.fileName, 50)</a></td>
                  <td>$!attachment.niceFileSize</td>
                  <td>#usernameLink($!attachment.creatorName)</td>
                  <td>$dateFormatter.formatDateTime($!attachment.creationDate)</td>
                  <td>$dateFormatter.formatDateTime($!attachment.lastModificationDate)</td>
                  <td>#parse("/labels/labels-editor-content.vm")</td>
                  <td class="attachedto">#contentLink2 ($!attachment.getContent() true false)</td>
            </tr>
   #end

2. In the line below:

   <td><a name="$!generalUtil.urlEncode($!attachment.content.displayTitle)-attachment-$!generalUtil.urlEncode($!attachment.fileName)">#parse ("/pages/includes/attachment_icon.vm")</a> <a href="$req.contextPath$!attachment.downloadPathWithoutVersion">$generalUtil.shortenString($attachment.fileName, 50)</a></td>

   add the parameter target="_blank" to the <a href> HTML tag, which will cause the URL specified in the href parameter to open in a new window or a new tag depending upon the option set in the browser. So the line above will be modified to:

   <td><a name="$!generalUtil.urlEncode($!attachment.content.displayTitle)-attachment-$!generalUtil.urlEncode($!attachment.fileName)">#parse ("/pages/includes/attachment_icon.vm")</a> <a href="$req.contextPath$!attachment.downloadPathWithoutVersion" target="_blank">$generalUtil.shortenString($attachment.fileName, 50)</a></td>

Open attachments listed for a Page

To open the page attachments listed from the Page's Attachment(s) tab, in a new window, the file <CONFLUENCE-INSTALL>/confluence/pages/includes/attachments-table.vm has to be modified. Below are the listed steps:

1. Locate the following block of code in the attachments-table.vm file:

   <td class="filename-column">
                   #parse ("/pages/includes/attachment_icon.vm")
                   <a class="filename" href="$generalUtil.htmlEncode("${req.contextPath}${attachment.downloadPathWithoutVersion}")"
                      title="$generalUtil.htmlEncodeAndReplaceSpaces($attachment.fileName)">
                       $generalUtil.htmlEncode($attachment.fileName)
                   </a>
               </td>

2. In the line below:

   <a class="filename" href="$generalUtil.htmlEncode("${req.contextPath}${attachment.downloadPathWithoutVersion}")"
   title="$generalUtil.htmlEncodeAndReplaceSpaces($attachment.fileName)">

   add the target="_blank" parameter to the <a href> HTML tag which will cause the URL specified in the href parameter to open in a new window.

   <a class="filename" href="$generalUtil.htmlEncode("${req.contextPath}${attachment.downloadPathWithoutVersion}")"
   title="$generalUtil.htmlEncodeAndReplaceSpaces($attachment.fileName)" target="_blank">

3. Locate the following block of code in the attachments-table.vm file:

   <td class="filename-column">
       <a class="filename" href="$generalUtil.htmlEncode("$req.contextPath$attachmentVersion.downloadPath")">#if ($velocityCount == 1)$action.getText("attach.file.version.current", $attachmentVersion.getVersion())#else$action.getText("attach.file.version.dated", $attachmentVersion.getVersion())#end</a>
   </td>

   and add the target="_blank" parameter to the <a href> HTML tag which will cause the URL specified in the href parameter to open in a new window.

   <td class="filename-column">
       <a class="filename" href="$generalUtil.htmlEncode("$req.contextPath$attachmentVersion.downloadPath")" target="_blank">#if ($velocityCount == 1)$action.getText("attach.file.version.current", $attachmentVersion.getVersion())#else$action.getText("attach.file.version.dated", $attachmentVersion.getVersion())#end</a>
   </td>

After making these changes, you'll need to restart Confluence for the changes to take effect.